Typically, as shown in FIG. 1, a wireless communication system 10 comprises elements such as client terminal or mobile station 12 and base stations 14. Other network devices which may be employed, such as a mobile switching center, are not shown. In some wireless communication systems there may be only one base station and many client terminals while in some other communication systems such as cellular wireless communication systems there are multiple base stations and a large number of client terminals communicating with each base station.
As illustrated, the communication path from the base station (BS) to the client terminal direction is referred to herein as the downlink (DL) and the communication path from the client terminal to the base station direction is referred to herein as the uplink (UL). In some wireless communication systems the client terminal or mobile station (MS) communicates with the BS in both DL and UL directions. For instance, this is the case in cellular telephone systems. In other wireless communication systems the client terminal communicates with the base stations in only one direction, usually the DL. This may occur in applications such as paging.
The base station with which the client terminal is communicating is referred to as the serving base station. In some wireless communication systems the serving base station is normally referred to as the serving cell. While in practice a cell may include one or more base stations, a distinction is not made between a base station and a cell, and such terms may be used interchangeably herein. The base stations that are in the vicinity of the serving base station are called neighbor cell base stations. Similarly, in some wireless communication systems a neighbor base station is normally referred to as a neighbor cell.
Duplexing refers to the ability to provide bidirectional communication in a system, i.e., from base station to client terminals (DL) and from client terminals to base station (UL). There are different methods for providing bidirectional communication. One of the commonly used duplexing methods is Frequency Division Duplexing (FDD). In FDD wireless communication systems, two different frequencies, one for DL and another for UL are used for communication. In FDD wireless communication system, the client terminals may be receiving and transmitting simultaneously.
Another commonly used method is Time Division Duplexing (TDD). In TDD based wireless communication systems, the same exact frequency is used for communication in both DL and UL. In TDD wireless communication systems, the client terminals may be either receiving or transmitting but not both simultaneously. The use of the Radio Frequency (RF) channel for DL and UL may alternate on a periodic basis. For example, in every 5 ms time duration, during the first half, the RF channel may be used for DL and during the second half, the RF channel may be used for UL. In some communication systems the time duration for which the RF channel is used for DL and UL may be adjustable and may be changed dynamically.
Yet another commonly used duplexing method is Half-duplex FDD (H-FDD). In this method, different frequencies are used for DL and UL but the client terminals may not perform receive and transmit operations at the same time. Similar to TDD wireless communication systems, a client terminal using H-FDD method must periodically switch between DL and UL operation. All three duplexing methods are illustrated in FIG. 2.
In many wireless communication systems, normally the communication between the base station and client terminals is organized into frames as shown in FIG. 3. The frame duration may be different for different communication systems and normally it may be on the order of milliseconds. For a given communication system the frame duration may be fixed. For example, the frame duration may be 10 milliseconds.
In a TDD wireless communication system, a frame may be divided into a DL subframe and a UL subframe. In TDD wireless communication systems, the communication from base station to the client terminal (DL) direction takes place during the DL subframe and the communication from client terminal to network (UL) direction takes place during UL subframe on the same RF channel.
Orthogonal Frequency Division Multiplexing (OFDM) systems typically use a Cyclic Prefix (CP) to combat inter-symbol interference and to maintain the subcarriers orthogonal to each other under a multipath fading propagation environment. The CP is a portion of the sample data that is copied from the tail part of an OFDM symbol to the beginning of the OFDM symbol as shown in FIG. 4. One or more OFDM symbols in sequence as shown in FIG. 4 are referred to herein as an OFDM signal.
In addition to the purposes mentioned above, the CP often may be used for frequency offset estimation at the receiver. Any frequency offset at the receiver relative to the center frequency of the transmitted signal may cause the phase of the received signal to change linearly as a function of time. The two parts of an OFDM signal that are identical at the transmitter, i.e., the CP and the tail portion of the OFDM symbol, may undergo different phase change at the receiver due to the frequency offset. Therefore, the frequency offset can be estimated by performing correlation between the CP and the tail portion of an OFDM symbol. The angle of the CP correlation indicates the amount of phase rotation that is accumulated over the duration of an OFDM symbol. This accumulated phase rotation may then used for frequency offset estimation. Let the incoming OFDM signal at a receiver be denoted by z(n) where n is the sample index. As illustrated in FIG. 4, let the length of an OFDM symbol, in terms of samples, excluding the CP portion, be denoted by N. Let the length of the CP portion, in terms of samples, be denoted by L. The CP correlation Rcp(n) at any sample index n may be computed as follows:
                                          R            cp                    ⁡                      (            n            )                          =                                                      1              L                        ⁢                                          ∑                                  l                  =                  0                                                  L                  -                  1                                            ⁢                                                z                  ⁡                                      (                                          n                      -                      l                                        )                                                  ·                                                      z                    *                                    ⁡                                      (                                          n                      -                      l                      -                      N                                        )                                                                                                                    (        1        )            where z* denotes complex conjugate of z and |•| denotes absolute value of its argument. Although the CP correlation may be computed for many different sample indices, it is expected to have a large value only for sample indices that correspond to the CP portion of the OFDM symbol. The largest CP correlation value in the duration over which CP correlation is performed may be considered for frequency offset estimation. The average power of the samples used for CP correlation may be computed as follows:
                                          P            cp                    ⁡                      (            n            )                          =                                            1              2                        ⁢                                          ∑                                  l                  =                  0                                                  L                  -                  1                                            ⁢                                                z                  ⁡                                      (                                          n                      -                      l                                        )                                                  ⁢                                                      z                    *                                    ⁡                                      (                                          n                      -                      l                                        )                                                                                +                                    z              ⁡                              (                                  n                  -                  l                  -                  N                                )                                      ⁢                                          z                *                            ⁡                              (                                  n                  -                  l                  -                  N                                )                                                                        (        2        )            The CP correlation values are normalized using the estimated power of the OFDM symbol samples used in CP correlation. Specifically, the normalized CP correlation is given as follows:
                                          r            cp                    ⁡                      (            n            )                          =                                            R              cp                        ⁡                          (              n              )                                                          P              cp                        ⁡                          (              n              )                                                          (        3        )            
Most wireless communication systems may employ some form of framing in the air interface. For example, 10 ms radio frames are used in the 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) wireless communication systems and each radio frame comprises 10 subframes as shown in FIG. 5. Each subframe in turn consists of two slots and each slot consists of 6 or 7 OFDM symbols depending on the type of CP used as shown in FIG. 6. In the 3GPP LTE wireless communication system, two different CP lengths are used and they are referred to as Normal CP and Extended CP. In wireless communication systems, normally the specific air interface frame structure repeats itself over certain periodicity.
The 3GPP LTE wireless communication system uses the following synchronization signals to assist the client terminal in achieving time and frequency synchronization as well as the detection of physical layer cell identity:                Primary Synchronization Signal (PSS)        Secondary Synchronization Signal (SSS)The positions of the PSS and SSS are illustrated in FIG. 6 for the FDD air-interface of a 3GPP LTE wireless communication system. Note that the FIG. 6 shows the position of the PSS and SSS for both the Normal CP and Extended CP. FIG. 7 illustrates the PSS and SSS positions for TDD air-interface of 3GPP LTE wireless communication system. The PSS and SSS signals for different cells may be different as described below.        
The different PSS and SSS are identified by different signal sequences used for transmission. Specifically, 504 physical cell identities are defined in 3GPP LTE wireless communication system specifications and they are organized into 168 groups with three identities in each group. The SSS sequence identifies the physical cell identity group and PSS sequence identifies the physical cell identity within a group. Detecting a physical cell identity requires the detection of both the PSS and the SSS.
The PSS sequence in frequency domain is a length 63 Zadoff-Chu sequence extended with five zeros on each side and mapped to central 72 sub-carriers as shown in FIG. 8. The Direct Current (DC) subcarrier is not used. In 3GPP LTE wireless communication system three different PSS sequences are used with Zadoff-Chu root indices 24, 29 and 34 corresponding to cell identity 0, 1 and 2 respectively within the physical cell identity group. The exact PSS sequences are defined in “3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (Release 12),” 3GPP TS 36.211 V12.8.0, December 2015, at Section 6.11, incorporated by reference herein. At the base station transmitter, the time domain PSS signal may be obtained by performing Inverse Discrete Fourier Transform (IDFT) of the frequency domain PSS. The two time domain PSS instances present within a 10 ms radio frame as shown in FIG. 7 and FIG. 8 are identical. The two SSS sequences present in a 10 ms radio frame are different, namely SSS1 and SSS2 as shown in FIG. 7 and FIG. 8, which allows the client terminal to detect 10 ms radio frame timing from the reception of a single SSS.
After PSS detection by a client terminal, frequency domain processing may be employed for further analysis, such as SSS search. The SSS search may have to handle timing and frequency offset ambiguities in addition to other system unknowns such as CP type and duplexing type. The relative timing (in terms of number of samples) between SSS and PSS varies depending upon CP and duplexing type. Multiple SSS search attempts may be required to resolve unknown system parameters such as CP type and duplexing type. If CP type is known prior to SSS detection, for example using a CP correlator, corresponding SSS detection attempts may be skipped. The PSS detection may result in multiple possible PSS positions being detected due to the presence of multiple cells surrounding the client terminal.
Frequency offset in OFDM systems generally manifests itself in two components commonly referred as integer frequency offset and fractional frequency offset. Integer frequency offset refers to the frequency offset in terms of an integral number of the subcarriers and the fractional frequency offset refers to the frequency offset remaining after excluding the integer frequency offset. In a 3GPP LTE wireless communication system the frequency spacing between subcarriers is 15 kHz. Therefore, for example, a frequency offset of 35 kHz at the client terminal manifests itself as two subcarrier offsets (30 kHz) plus a fractional frequency offset of 5 kHz. Since the subcarrier spacing is 15 kHz, the maximum fractional frequency offset may be half of the subcarrier spacing of 15 kHz. Therefore, the range of possible fractional frequency offset values may be in the range±7500 Hz.
Fractional frequency offset may be compensated by estimating it using conventional methods such as CP correlation. In conventional systems, the integer frequency offset may be detected in the frequency domain by attempting to decode SSS with different hypotheses about different SSS frequency bin positions.
One of the commonly used methods for PSS detection is the cross correlation of the received signal with the local replica for the three possible candidates. However, the structure of the 3GPP LTE wireless communication system air interface synchronization signal PSS is such that the presence of frequency offset causes a shift in the apparent detected timing position of the PSS.
In PSS detection, the incoming signal may be cross correlated with the local replica of the PSS sequence for all three root sequence indices. Let the local replica of the PSS signal for the mth PSS root sequence index be denoted by pm(n) with m=0, 1, or 2. Let the incoming signal be denoted by z(n). The cross correlation between these two signals is computed as follows:
                                          R                          PSS              ⁢                                                          ⁢              _              ⁢                                                          ⁢              m                                ⁡                      (            n            )                          =                                                      1              K                        ⁢                                          ∑                                  k                  =                  0                                                  K                  -                  1                                            ⁢                                                z                  ⁡                                      (                                          n                      -                      k                                        )                                                  ·                                                      p                    m                    *                                    ⁡                                      (                                          K                      -                      k                                        )                                                                                                                    (        4        )            where K is the length of the PSS local replica signal at the sampling rate of the incoming signal z(n).
The cross correlation peaks at a time instant when the incoming signal aligns and matches with one of the three replicas as illustrated in FIG. 9. The location of this cross correlation peak is used as an indicator of the PSS position and that position is used as a reference for subsequent SSS detection. The X-axis in FIG. 9 indicates the location of the detected peak relative to the true PSS time position.
When the cross correlation is performed with the received signal that has a frequency offset relative to the receiver's frequency, the cross correlation peak shifts as a function of the frequency offset as illustrated in FIG. 10. As illustrated in FIG. 10, the magnitude of the cross correlation peak reduces if a frequency offset is present. Furthermore, the location of the peak may be shifted relative to the true position as illustrated in FIG. 10. There may be multiple peaks of comparable magnitude at respective different time positions relative to the true position for a single received signal with a single frequency offset as illustrated in FIG. 10.